Mathematics Enthusiast最新文献_第9页

An Analysis of the Influences of a Hybrid Learning Environment in the Solution of Vector Tasks according to the Anthropological Theory of the Didactic (ATD) 从教学人类学理论分析混合学习环境对向量任务求解的影响

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Mathematics Enthusiast Pub Date : 2021-08-01 DOI: 10.54870/1551-3440.1540

Jany Santos Souza Goulart, Luiz Márcio Santos Farias, Hamid Chaachoua

{"title":"An Analysis of the Influences of a Hybrid Learning Environment in the Solution of Vector Tasks according to the Anthropological Theory of the Didactic (ATD)","authors":"Jany Santos Souza Goulart, Luiz Márcio Santos Farias, Hamid Chaachoua","doi":"10.54870/1551-3440.1540","DOIUrl":"https://doi.org/10.54870/1551-3440.1540","url":null,"abstract":"This paper discusses a part of a doctoral study based on the theoretical pillars of the Anthropological Theory of the Didactic (ATD). Supported by this theory, our research interest followed a path that led us to the teaching of the mathematical object vector and its institutional configuration in a Mathematics Teaching course at Universidade Estadual de Feira de Santana (UEFS), in the state of Bahia, Brazil, centered on two dichotomous aspects. The first one refers to the possibility of application and institutional relevance of this mathematical object. The second aspect is related to the obstacles encountered in the didactical scope, which have impact on the teaching/learning of this mathematical object. In this discussion, the question that guided our investigation emerged: how to harness praxeological recombinations that can promote mediation between personal and institutional relationships in the scope of vector knowledge in the Mathematics Teaching course at UEFS? Based on this context, we aim at analyzing students’ productions in terms of solution paths to a vector task in a Hybrid Learning Environment (HLE), from a developmental perspective based on the T4TEL didactical framework (Chaachoua, 2018). With regard to methodological support, Didactical Engineering provided directions that enabled us to make a comparison between a priori and a posteriori analyses, resulting in the identification of the reach of the techniques that were developed in contrast to the naturalized techniques that are part of this context.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47138985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Editorial: The Planet’s Pandemic Pandemonium 社论：地球的大流行病

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1508

Bharath Sriraman

引用次数: 0

The Suuji Approach to Multi-Digit Addition: Using Length to Deepen Students’ Understanding of the Base 10 Number System 数位加法的Suuji法:用长度加深学生对十进制的理解

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1526

R. Matsuura, O. Hall-Holt, Nancy Dennis, Michelle Martin, Sarah Sword

引用次数: 0

Archimedes’ Works in Conoids as a Basis for the Development of Mathematics 阿基米德的圆锥体著作是数学发展的基础

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1519

Kenton Ke

引用次数: 0

Indigenous Culture-Based School Mathematics in Action Part II: The Study’s Results: What Support Do Teachers Need? 基于本土文化的学校数学在行动第二部分:研究结果:教师需要什么支持?

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1517

Sharon Meyer, G. Aikenhead

{"title":"Indigenous Culture-Based School Mathematics in Action Part II: The Study’s Results: What Support Do Teachers Need?","authors":"Sharon Meyer, G. Aikenhead","doi":"10.54870/1551-3440.1517","DOIUrl":"https://doi.org/10.54870/1551-3440.1517","url":null,"abstract":"This second part of two related articles reports the answers to the research question: What precise supports must be in place for Grades 5 to 12 teachers to enhance their mathematics classes in a sustainable way with Indigenous mathematizing and Indigenous worldview perspectives? In addition to various logistical supports, two other types of supports were identified: supports for learning and unlearning ways of perceiving the world generally and perceiving Western mathematics specifically. These needed supports came to light when we mentored the teachers. On the one hand, the co-researching teachers learned, or had already learned: (a) the plurality of mathematical systems; (b) the perspective of Western mathematics as a human endeavor along with its values, ideologies, and definitions; (c) the mere inclusion of Indigenous mathematizing in a lesson is not enough; and (d) the goal of two-eyed seeing. On the other hand, the co-researching teachers unlearned, or had already unlearned: (a) pure mathematics’ claim to be value-free, (b) all students have a predilection to excel at mathematics, and (c) subtle appropriation committed by many mathematics educators as if it were common sense to do it.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45249724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

Impediments to mathematical creativity: Fixation and flexibility in proof validation 数学创造力的障碍:证明验证的固定和灵活性

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1518

P. Haavold

引用次数: 4

Flattening the Curve 曲线变平

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1527

P. Zizler, Mandana Sobhanzadeh

引用次数: 30

Beauty is in the blind spot of the beholder 情人眼里出西施

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1522

Ron Aharoni

{"title":"Beauty is in the blind spot of the beholder","authors":"Ron Aharoni","doi":"10.54870/1551-3440.1522","DOIUrl":"https://doi.org/10.54870/1551-3440.1522","url":null,"abstract":": The paper addresses the time-old question of what is beauty. A rather ambitious, if not to say presumptuous, endeavour. But I do not aim high – I do not claim to get anywhere near unearthing the secret. Rather, I will use examples from mathematics, poetry, music and chess to substantiate one thesis: that the elusory character of beauty is not incidental. Its defiance of definition is part of its essence. The aesthetic sensation requires unawareness of its precise origin. Beauty is felt when some order is perceived, that is not fully comprehended. The order is too complex, or well hidden, or too novel, to surface in its entirety. This is the reason for our ability to enjoy a piece of art for the hundredth time – we never fully fathom its inner order. This is also the reason for the feeling of awe that the beauty inspires: mystery and magic are at its heart. I will compare mathematical techniques and features with those of poetry - like compression, summoning patterns from one field to solve problems in another, or self-reference, and show how beauty is generated in the two domains in a similar way. I will also comment on the beauty-generating effect of unexpectedness in both domains. That novelty generates beauty is a trite observation (“the most expected feature of a poem is its unexpectedness”, as somebody put it), but the question why this is so is not often addressed – I will connect it with the “blind spot” idea. In a final section I try to answer the question that is at least as difficult as “what is beauty” – “why beauty?”. The fact that it pervades our lives indicates that it has an important role – what is it? To arouse the reader’s curiosity, let me summarize the attempted answer in one word – ‘change’. That aim that is so coveted and so hard to achieve – a change in the pattern of our actions, aims and perceptions. The style of the paper is non-scientific, and non-erudite, reflecting my belief that scientific pretensions in the humanities deflect from “softer”, more genuine, understanding.","PeriodicalId":44703,"journal":{"name":"Mathematics Enthusiast","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49017886","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A formal justification of the Ancient Chinese Method of Computing Square Roots 中国古代计算平方根方法的形式论证

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1513

Edilberto Nájera, Leslie Cristina Najera-Benitez

引用次数: 0

Using Records of Practice to Bridge from Teachers’ Mathematical Problem Solving to Classroom Practice 用实践记录架起教师数学解题与课堂实践的桥梁

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Mathematics Enthusiast Pub Date : 2021-01-01 DOI: 10.54870/1551-3440.1523

D. Fischman, I. Riggs

引用次数: 1